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Hope College Prep High School: Geometry Curriculum Map 2014-2015 Teacher First and Last Name Maurice P. Schwartz Course Geometry Subject Area Mathematics Grade Level 10 Units Calendar Unit 1 Title Foundations for Geometry Dates (school calendar weeks) Sep 2 - Sep 30 Unit 2 Title Parallel and Perpendicular Lines Dates (school calendar weeks) Oct 1 - Oct 29 Unit 3 Title Triangle Congruence Dates (school calendar weeks) Oct 30 - Dec 12, Q Unit 4 Title Properties of Triangles Dates (school calendar weeks) Dec 15 - Jan 26 Unit 5 Title Polygons and Quadrilaterals Dates (school calendar weeks) Jan 27 - Feb 25, Q Unit 6 Title Similarity Dates (school calendar weeks) Feb 26 - Mar 25 Unit 7 Title Right Triangles and Trigonometry Dates (school calendar weeks) Mar 26 - May 7, Q Unit 8 Title Circles Dates (school calendar weeks) May 8 - Jun 16, Q Unit 1 Summary + Curriculum Alignment Unit Title Foundations for Geometry Major Topics Understanding points, lines, planes, angles, segments, midpoint, and distance in the coordinate plane. Description of Find the distance between two vertices of a rectangle in the coordinate plane. Primary Performance Task NOTE: One task per unit Common Core Standard(s) Related to Task G-CO.1: Experiment with transformations in the plane. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. CRS Supporting Skills College Bound GR 20-23 401 GR 24-27 504 Accelerated GR 20-23 401 GR 24-27 504 Honors GR 20-23 401 GR 24-27 504 GR 28-32 603 Industry or Subject Specific Standards Interdisciplinary Integrations / Thematic Connections Algebra: Unit Conversions Connections to Writing Framework Find an unfamiliar term and write the definition in their student journal. Cornell Notes Summary Assessment Supplementary Text Diagnostic/ Pre-Assessment Using a protractor, measure an acute angle in degrees. Formative Problem of the Day, Questions and Answers, Classwork, Group Work, Quizzes, Homework, Discovery Activities Summative Tests, MARS Task Description/ Title Geometry Foundations V3.0 Units 1-5 Lexile Flesch Reading Ease Nonfiction, Informational Informational Flesch-Kincaid Reading Level Framing Questions Essential Question(s) How does knowledge of geometry help in your everyday life? Unit Content Questions Explain why we can only draw representations of points, lines and planes. What are the “essential components” of angles? Explain midpoint and distance in the coordinate plane. Unit 2 Summary + Curriculum Alignment Unit Title Parallel and Perpendicular Lines Major Topics Parallel and Perpendicular Lines, Angles Formed by Parallel Lines and Transversals, Slope. Description of Primary Performance Task Find which angles, formed by two parallel lines cut by a transversal, are congruent and which angles are supplementary. NOTE: One task per unit Common Core CC.9-12.G.CO.9 Prove geometric theorems. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are Standard(s) Related to Task congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. CC.9-12.G.CO.12 Make geometric constructions. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. CC.9-12.G.GPE.5 Use coordinates to prove simple geometric theorems algebraically. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). CRS Supporting College Skills Bound PPF 16-19 301 PPF 20-23 401 GR 20-23 403 Accelerated PPF 16-19 301 PPF 20-23 401 GR 20-23 403 Honors GR 28-32 604 PPF 16-19 301 PPF 20-23 401 GR 20-23 403 Industry or Subject Specific Standards Interdisciplinar y Integrations / Algebra: Equations of Lines in the Coordinate Plane Thematic Connections Connections to Find an unfamiliar term and write the definition in their student journal. Writing Cornell Notes Summary Framework Assessment Diagnostic/ Pre-Assessment Using a protractor, draw a right angle. Formative Problem of the Day, Questions and Answers, Classwork, Group Work, Quizzes, Homework, Discovery Activities Summative Tests, MARS Task Supplementary Description/ Title Geometry Nonfiction, Informational Informational Text Foundations V3.0 Units 1-5 Flesch Reading Ease Lexile Flesch-Kincaid Reading Level Framing Questions Essential Question(s) What would “things” look like without parallel and perpendicular lines? Unit Content Questions What angles are formed when parallel lines are cut by a transversal? Unit 3 Summary + Curriculum Alignment Unit Title Triangle Congruence Major Topics Classifying Triangles, Angle Relationships in Triangles, Triangle Congruence Postulates Description of Primary Performance Task What is the least amount of information needed to show that two triangles are congruent? NOTE: One task per unit Common Core CC.9-12.G.CO.8 Understand congruence in terms of rigid motions. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Standard(s) Related to Task CC.9-12.G.CO.10 Prove geometric theorems. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. CRS Supporting College Skills Bound PPF 24-27 501, 503 PPF 20-23 402 Accelerated PPF 24-27 501, 503 PPF 20-23 402 Honors PPF 24-27 501, 503 PPF 20-23 402 Industry or Subject Specific Standards Interdisciplinar y Integrations / Algebra: Quadratic Equations Thematic Connections Connections to Find an unfamiliar term and write the definition in their student journal. Writing Cornell Notes Summary Framework Assessment Diagnostic/ Pre-Assessment Using a straight edge and compass, draw two congruent triangles. Formative Problem of the Day, Questions and Answers, Classwork, Group Work, Quizzes, Homework, Discovery Activities Summative Tests, MARS Task Supplementary Text Description/ Title Geometry Foundations V3.0 Nonfiction, Informational Units 1-5 Flesch Reading Ease Lexile Informational Flesch-Kincaid Reading Level Framing Questions Essential Question(s) Where are triangles so important? Unit Content Questions What is the least amount of information needed to show that two triangles are identical? Why is this important? Unit 4 Summary + Curriculum Alignment Unit Title Properties of Triangles Major Topics Perpendicular and Angle Bisectors, Midsegments, Pythagorean Theorem. Description of Primary Performance Task What are Pythagorean triples? NOTE: One task per unit Common Core CC.9-12.G.CO.9 Prove geometric theorems. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are Standard(s) Related to Task congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. CC.9-12.G.CO.12 Make geometric constructions. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. CRS Supporting College Skills Bound M 13-15 201 PPF 20-23 402 PPF 24-27 501 Accelerated M 13-15 201 PPF 20-23 402 PPF 24-27 501 Honors PPF 28-32 602 M 13-15 201 PPF 20-23 402 PPF 24-27 501 Industry or Subject Specific Standards Interdisciplinar y Integrations / Algebra: Solving Equations with Radicals. Thematic Connections Connections to Find an unfamiliar term and write the definition in their student journal. Writing Cornell Notes Summary Framework Assessment Supplementary Text Diagnostic/ Pre-Assessment Using a compass and straight edge, bisect a line segment. Formative Problem of the Day, Questions and Answers, Classwork, Group Work, Quizzes, Homework, Discovery Activities Summative Tests, MARS Task Description/ Title Geometry Foundations V3.0 Nonfiction, Informational Units 1-5 Flesch Reading Ease Lexile Informational Flesch-Kincaid Reading Level Framing Questions Essential Question(s) What would “things” look like without right angles? Unit Content Questions What is the least amount of information needed to solve each type of triangle? Unit 5 Summary + Curriculum Alignment Unit Title Polygons and Quadrilaterals Major Topics Properties of Polygons, Parallelograms, and Quadrilaterals. Description of Primary Performance Task How do you find the perimeter of a parallelogram? NOTE: One task per unit Common Core CC.9-12.G.CO.11 Prove geometric theorems. Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect Standard(s) Related to Task each other, and conversely, rectangles are parallelograms with congruent diagonals. CRS Supporting College Skills Bound M 13-15 201 M 16-19 301,302 PPF 24-27 501 M 20-23 401 M 24-27 501,503 Accelerated M 13-15 201 M 16-19 301,302 PPF 24-27 501 M 20-23 401 M 24-27 501,503 Honors M 13-15 201 M 16-19 301,302 PPF 24-27 501 M 20-23 401 M 24-27 501,503 Industry or Subject Specific Standards Interdisciplinar y Integrations / Algebra: Solving a Formula for a Variable Thematic Connections Connections to Find an unfamiliar term and write the definition in their student journal. Writing Cornell Notes Summary Framework Assessment Supplementary Text Diagnostic/ Pre-Assessment Use the Pythagorean theorem to find the diagonal of a rectangle. Formative Problem of the Day, Questions and Answers, Classwork, Group Work, Quizzes, Homework, Discovery Activities Summative Tests, MARS Task Description/ Title Geometry Foundations V3.0 Units 1-5 Flesch Reading Ease Lexile Nonfiction, Informational Informational Flesch-Kincaid Reading Level Framing Questions Essential Question(s) What does the word “polygon” mean? Unit Content Questions What information about triangles can be used to solve polygons? Unit 6 Summary + Curriculum Alignment Unit Title Similarity Major Topics Ratio and Proportion, Triangle Similarity Postulates, Indirect Measurement Description of How do you measure the height of a tree? Primary Performance Task NOTE: One task per unit Common Core Standard(s) Related to Task CC.9-12.G.SRT.2 Understand similarity in terms of similarity transformations. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. CC.9-12.G.SRT.3 Understand similarity in terms of similarity transformations. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. CRS Supporting Skills College Bound PPF 24-27 501 Accelerated PPF 24-27 501 Honors BOA 33-36 701 PPF 24-27 501 PPF 28-32 601 Industry or Subject Specific Standards Interdisciplina ry Integrations / Algebra: Direct Variation Thematic Connections Connections to Writing Framework Assessment Find an unfamiliar term and write the definition in their student journal. Cornell Notes Summary Diagnostic/ Pre-Assessment Use cross-products to solve a proportion. Formative Problem of the Day, Questions and Answers, Classwork, Group Work, Quizzes, Homework, Discovery Activities Summative Tests, MARS Task Description/ Title Geometry Foundations V3.0 Units 1-5 Supplementar y Text Nonfiction, Informational Flesch Reading Ease Lexile Informational Flesch-Kincaid Reading Level Framing Questions Essential Question(s) How could you measure the height of an inaccessible object? Unit Content Questions What is the least amount of information needed to show two triangles are similar? Why is this important? Unit 7 Summary + Curriculum Alignment Unit Title Right Triangle Trigonometry Major Topics Trigonometric Ratios, Solving Right Triangles Description of Primary Performance Task How do you measure the height of a skyscraper? NOTE: One task per unit Common Core CC.9-12.G.SRT.8 Define trigonometric ratios and solve problems involving right triangles. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Standard(s) Related to Task CRS Supporting College Skills Bound Accelerated F 24-27 50 F 24-27 502 Honors F 24-27 502 F 28-32 602 F 33-36 702 Industry or Subject Specific Standards Interdisciplinar y Integrations / Algebra: Inverse Functions Thematic Connections Connections to Find an unfamiliar term and write the definition in their student journal. Writing Cornell Notes Summary Framework Assessment Supplementary Text Diagnostic/ Pre-Assessment Using a calculator, find the ratio of two numbers. Formative Problem of the Day, Questions and Answers, Classwork, Group Work, Quizzes, Homework, Discovery Activities Summative Tests, MARS Task Description/ Title Geometry Foundations V3.0 Units 1-5 Nonfiction, Informational Flesch Reading Ease Lexile Informational Flesch-Kincaid Reading Level Framing Questions Essential Question(s) What does the word “trigonometry” mean? Unit Content Questions Why is the Pythagorean Theorem so useful? Unit 8 Summary + Curriculum Alignment Unit Title Circles Major Topics Lines and Arcs in Circles, Angles and Segments in Circles. Description of Primary Performance Task How do you find the area of a sector? NOTE: One task per unit Common Core CC.9-12.G.C.2 Understand and apply theorems about circles. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed Standard(s) Related to Task angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. CC.9-12.G.C.5 Find arc lengths and areas of sectors of circles. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. CRS Supporting College Skills Bound M 24-27 502 M 13-15 201 Accelerated M 24-27 502 M 13-15 201 Honors M 24-27 502 PPF 33-36 703 M 13-15 201 Industry or Subject Specific Standards Interdisciplinar y Integrations / Data Analysis: Circle Graphs Thematic Connections Connections to Find an unfamiliar term and write the definition in their student journal. Writing Cornell Notes Summary Framework Assessment Supplementary Text Diagnostic/ Pre-Assessment How does the area of a circle change if you double the diameter? Formative Problem of the Day, Questions and Answers, Classwork, Group Work, Quizzes, Homework, Discovery Activities Summative Tests, MARS Task Description/ Title Geometry Foundations V3.0 Units 1-5 Lexile Nonfiction, Informational Flesch Reading Ease Framing Questions Essential Question(s) What special number is so essential with circles? Unit Content Questions What are two important segments inside a circle? Informational Flesch-Kincaid Reading Level